It is often desirable to "zoom in" on or otherwise change the size of an MRI image (e.g., to provide more detailed views of structures of interest). Such "zooming" is not generally straight-forward or easy to accomplish, however, due to a correspondence between the number of time domain (raw data) samples within the time domain data set and the number of pixels defined by the spatial (image) domain data resulting from Fourier Transformation.
The fundamentals of the MRI experiment are well known. Briefly (and hopefully without undue oversimplification), in a typical MRI system an object 10 (see FIG. 1) to be imaged (e.g., a portion of the human body) is placed in an external static magnetic field gradient. Protons within the object tend to align their spins in accordance with the magnetic field direction. The object is excited by one or more RF excitation pulses of appropriate frequency, timings and durations (as one example, so-called "spin-echo" type pulse sequences may be used). The RF excitation pulses generated at the Larmour frequency cause the protons to precess their spins. When each RF pulse is switched off, the nucleii precess back toward their equilibrium position and in this relaxation process emit an NMR response that can be detected by an RF receiver.
In most imaging applications the NMR responses are spatially encoded by applying different magnetic field gradients during excitation, readout and in between. For example, two-dimensional spatial encoding may be provided using the so-called "spin warp" technique in which frequency information within the NMR responses store spatial information in one dimension (e.g., the x direction), and the phase component of the NMR responses store spatial information in the other dimension (e.g., the z direction). Using this technique, a readout gradient (e.g., Gx) is switched on during readout to frequency encode the spatial information in the one dimension (e.g., x); and another gradient (e.g., Gz) is switched on during the so-called "evolution" period (between the excitation period and the readout period) to phase encode the NMR pulses in the other dimension (e.g., z). The amplitude or duration of the phase encoding gradient is typically changed during a scan to provide different variations in phase angle for each NMR signal detected.
During the readout period, the NMR signal is typically sampled at regular time intervals .tau. to provide a time domain raw data set of Fourier coefficients S(t.sub.O, .tau.), S(t.sub.O, 2.tau.), S(t.sub.O, 3 .tau.) . . . S(t.sub.O, n.tau.)--the value of .tau. being chosen to conform to the sampling theorem (i.e., the sampling rate is at least twice the highest frequency component present in the signal). A sampling rate that is too low will generally result in a frequency interval that is too coarse--causing the object to fill only a small portion of the image field. Too high a sampling rate will result in aliasing the high frequency signals (thus folding them back into the low frequency part of the spectrum). The total number of sample points (Fourier coefficients) determines the spatial resolution after Fourier transformation (typically in two dimensions) and is usually chosen to be a power of 2 in order to take advantage of FFT (fast Fourier Transform) techniques. The resulting set of raw NMR time-domain data is generally symmetrical in both dimensions (e.g., x and z) and thus constitutes an N.times.N array of time-domain values.
The time domain data set may be further manipulated in a well known manner for a variety of reasons (e.g., to correct for instrumentation error, to improve signal-to-noise ratio, etc.)
The term "reconstruction" describes the process by which the acquired time-domain data set is converted into an image of the object. A two-dimensional Fourier transform (FT) is applied to the time-domain data set as described above to extract the frequency and phase information (and thus the spatial encoding) to develop spatial domain data (see FIG. 1). This spatial domain data may then be further processed using conventional techniques to provide an image on an electronic display and/or stored in a data file for later retrieval and imaging.
The sampling interval .tau. used during image acquisition generally establishes spatial resolution (i.e., the number of pixels) of the spatial domain data set--since sampling interval determines the spatial distribution corresponding to the Fourier coefficients and thus establishes the coordinate points of a "grid" of slice-volumes defined within the object space. Thus, in general it has been necessary to gather a 256.times.256 raw data array in order to provide a reconstructed image comprising 256.times.256 pixels. It was known in the past, however, to alter in a limited manner this essentially one-to-one correspondence between number of acquired time-domain samples and the number of values in the spatial domain.
For example, it is known to add zero values to the raw data set (a technique called "zero filling") in one or more dimensions to take advantage of the resulting improvement in image "resolution" (i.e., to increase the total number of pixels per line in images) without a concomitant increase in acquisition time. This technique involves adding zero "high frequency" components (i.e , zero values around the "outside" of the time domain data set array). This zero filling technique was also used to reduce acquisition time by increasing the signal-to-noise ratio of "high frequency" image components without degrading image "resolution" or computation time. See Batholdi et al, 11 Journal of Magnetic Resonance 9 (1973).
Many in the past have sought to provide "zooming" capability for MRI. The following is a non-exhaustive listing of prior issued U.S. Patents relating to advantages of and techniques for MRI image "zooming":
U.S. Pat. No. 4,703,271 to Loeffler et al; PA1 U.S. Pat. No. 4,644,280 to Paltiel; and PA1 U.S. Pat. No. 4,593,247 to Glover.
Many prior art zooming techniques provided altered RF pulse sequences and/or other acquisition parameters. For example, the Glover patent discloses a technique in which NMR signals are band-limited prior to conversion by the A/D converter so as to band limit the NMR signal in the X and Y axis directions. "Zooming" in on off center regions is accomplished by shifting the receiver frequency. The technique disclosed in the Paltiel patent avoids aliasing artifacts to allow image zooming by using a pseudo spin echo sequence.
The technique of "interpolation" may also be used to accomplish "zooming." Interpolation permits values of the image at coordinate points different from those imposed by the sampling interval to be ascertained. Such image interpolation techniques are extremely useful in allowing greater flexibility in changing image appearance without requiring new data to be acquired. Interpolation may be used in conjunction with resampling to "zoom" in on an image (i.e., to provide an image in which there is more than one pixel for each time-slice imposed by the sampling interval). Unfortunately, interpolation techniques may sometimes add artifacts to the "zoomed in" image.
Interpolating an image generally involves fitting a continuous function to the discrete points in the digital image so that values are defined at coordinate points other than those predetermined by the sampling interval. The continuous function may then be resampled at arbitrary points of interest. Interpolation and sampling can be combined so that the signal is interpolated only at those points which will be sampled during the resampling process.
But interpolation and resampling can sometimes introduce troublesome artifacts that cause the zoomed image to lose clarity. For example, the assignee of the subject application has in the past provided zooming capability through a technique of linear interpolation of spatial domain (image) data followed by resampling the interpolated data so as to provide more pixel values than were provided by the sampling interval used during data acquisition. While this technique can provide a "zoomed in" image (i.e., an image that is enlarged in size with respect to the original image provided without interpolation), the interpolation/resampling process can introduce image artifacts (see FIG. 7A for example). Much work has been done in the past toward finding better interpolating functions to use in MRI. Parker et al in "Comparison of MI-2, No. 2, IEEE Transactions on Medical Imaging (March 1983) survey a variety of different interpolating functions and discuss the advantages and disadvantages of each. See also Maeland, "On the Comparison of Interpolation Methods", Vol. 7, No. 3 IEEE Transactions on Medical Imaging (Sept. 1988). While better interpolation techniques might possibly be used to reduce such artifacts, such better interpolation techniques may also introduce computational complexity requiring additional processing resources and/or longer processing time. More computationally-efficient yet flexible techniques for resizing MRI images would therefore be highly advantageous.
A different approach to interpolation is described in a commonly assigned now allowed patent application Ser. No. 07/293,859 of Kaufman et al filed 5 Jan. 1989 entitled "3D Image Reconstruction Method for Placing 3D Structure Within Common Oblique or Contoured Slice-Volume Without Loss of Volume Resolution". That commonly-assigned patent application discloses a Fourier Transformation image reconstruction interpolation technique in which the boundaries of a slice-volume can effectively be shaped in three dimensions. The Kaufman et al technique involves applying the Fourier Shift theorem to time-domain data during Fourier Transformation to result in pixel shifts in the spatial domain.
The present invention is directed to a further improvement in Fourier Transformation MRI image reconstruction techniques, and more specifically, provides an interpolation technique which changes the size of the MRI image that can be produced from a given time domain data set without suffering from the disadvantages which arise from interpolating and resampling spatial domain data.
In accordance with one aspect of this invention, a two-dimensional array of MRI "raw data" time domain data set (e.g., digitized NMR signals acquired by an analog-to-digital converter) is conceptually defined within a larger two-dimensional array in which all points within the larger array not defined by the time domain data set are set to a zero value (i.e., higher frequency components than those acquired by the sampling are defined and set to zero). The size of the larger array is selected to provide a desired "zoom factor." The larger array (including the "zero padded" values) are then processed using Fourier transformation techniques (e.g., Fourier transformation in two dimensions) to produce spatial domain data. The resulting spatial domain data defines an image which is resized with respect to an image produced if the original time domain data set had been processed in the normal manner using Fourier Transformation.
In accordance with one feature of the present invention, the "raw data" time domain data set generated during acquisition is Fourier Transformed without "zero padding" to produce spatial domain data. The spatial domain data may be displayed to provide an "original" image. The spatial domain data is stored, and the "raw data" time domain data set is discarded. If a magnified ("zoomed", "enlarged" or "blown up") view of a structure of interest within the "original" image is desired, the operator selects a zoom factor and initiates a zooming function. Spatial domain data is subjected to inverse Fourier Transformation (e.g., in two dimensions) to regenerate a time domain data set. The regenerated time domain data set is then "zero padded" and Fourier transformed (e.g., Fourier transformed in two dimensions with the limits of the Fourier Transformation being set to be larger than the actual extents of the time domain data set by an amount determined in response to the operator-selected "zoom factor") to provide new spatial domain data. The new spatial domain data resulting from the Fourier Transformation may then be displayed to provide an "enlarged" view--with the amount of magnification as compared with the "original" image depending upon the selected limits for the Fourier Transformation.
In accordance with another embodiment of the present invention, the original time domain data set provided by the analog-to-digital converter is not discarded after Fourier Transformation (as is the normal practice) but is instead stored for later use if magnification is required. If desired, the time domain data set may be processed using Fourier Transformation in the conventional manner for display; and the resulting spatial domain data and the time domain data set may both be stored. If display of the conventionally sized image is desired at a later time, that display may be generated from the spatial domain data. If, on the other hand the operator wishes to display a resized image, the zero padding/Fourier Transformation technique described above is applied to the stored time domain data set to produce a resized image.
A further aspect of the present invention involves selecting a zoom factor value (e.g., by an operator on an interactive basis) and calculating a size for the zero-padded time domain data array based on the selected zoom factor. The zoom factor value and resulting corresponding zero padded time domain array size may thus be varied at will (e.g., on an interactive basis) to provide different sized images.
A further aspect of the present invention relates to restricting zoom factor values so as to minimize computation time. In accordance with this further feature of the present invention, only certain zoom factors are preferably used so as to permit use of the fast Fourier Transform (FFT). Assume that the size of the larger "zero padded" array is M.times.M where M is an integer. If M=2.sup.n (i.e., M is a power of 2), it is possible to use FFT to process the zero padded time domain data set. However, being restricted to M being a power of 2 may be somewhat inflexible for some applications since it limits the number of different zoom factors that may be used. In accordance with a further aspect of this invention, certain additional integer values for M may also permit use of FFT. For example, M may be in the form of M=2 .sup.p 3.sup.q ; M=2.sup.p 5.sup.q ; or M=2.sup.p 3.sup.q 5.sup.r where p, q (and r) are each integers. Each of these forms for M also permits use of FFT for fourier transformation of the zero padded time domain data set--thus providing additional flexibility in selecting zoom factors while nevertheless also providing the increase in computational efficiency offered by FFT.